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drek231 [11]
3 years ago
10

Write the equation of each line using the given information.

Mathematics
1 answer:
Leni [432]3 years ago
6 0

a) x – 2y + 6 = 0 b) x + y = 1 c) y = 1 d) y = -3x + 8

<h3><u>Solution:</u></h3>

<em><u>a. The points (-4,1) and (2,4) both lie on the line</u></em>

The general line equation on which (a, b) and (c, d) lies is:

y-\mathrm{b}=\frac{d-b}{c-a}(x - a)

Here the given points are (a, b) = (-4, 1) and (c, d) = (2, 4)

Thus the required equation is:

y-1=\frac{4-1}{2-(-4)}(x-(-4))

On solving we get,

\begin{array}{l}{\rightarrow y-1=\frac{3}{2+4}(x+4)} \\\\ {\rightarrow y-1=\frac{3}{6}(x+4)} \\\\ {\rightarrow 2(y-1)=1(x+4)} \\\\ {\rightarrow 2 y-2=x+4} \\\\ {\rightarrow x-2 y+6=0}\end{array}

<em><u>b.) m= -1 and the point (2, -1) lies on the line</u></em>

The equation of line in point slope form is y – b = m(x – a)  

where m is slope and (a, b) is a point on it

Here m = -1 and (a, b) = (2, -1)

Thus the required equation is:

y – (-1) = -1(x - 2)  

y + 1 = -x + 2  

y = -x + 2 -1  

y = -x + 1

<em><u>c. )It has the same slope as y = 5 and passes through (1, 1)</u></em>

our line has same slope with y = 5, then our equation would be y = k  and it passes through (x, y) = (1, 1) so, then by substitution

1 = k

k =1  

Then our equation will be y = k

y = 1

<em><u> d. ) m= -3 and it has a y-intercept of (0, 8)</u></em>

line equation in slope intercept form is y = mx + b where m is slope and b is y – intercept.

Then, our equation will be y = -3x + 8

We took y- intercept = 8 as it is the value of y when x = 0

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How do i write a two column proof for this??<br><br>Given: PG ≅ SG and PT ≅ ST . Prove: ∠GPT ≅ ∠GST
Nikolay [14]

Answer:

PG ≅ SG (Given)

PT ≅ ST (Given)

GT = GT (Common)

∴ ∠GPT ≅ ∠GST (SSS Congruency Axiom)

Step-by-step explanation:

<u>Given</u>: PG ≅ SG and PT ≅ ST

<u>To Prove</u>: ∠GPT ≅ ∠GST

<u>Proof</u>:  PG ≅ SG (Given)

PT ≅ ST (Given)

GT = GT (Common)

∴ ∠GPT ≅ ∠GST (SSS Congruency Axiom).

<u>SSS Congruency Axiom</u>:  If three pairs of sides of two triangles are equal in length, then the triangles are congruent.

<u>Congruence</u>: Two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

7 0
3 years ago
PLEASE ANSWER THIS QUESTION AND EXPLAIN IF YOU CAN
jekas [21]
Factor out -1
-1(x^2+x-6)

Factor the inner trinomial
-1(x+3)(x-2)

Final answer: B
6 0
3 years ago
Read 2 more answers
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